On the stability of radical septic functional equations.

This paper deals with the approximate solution of the following functional equation f x 7 + y 7 7 = f (x) + f (y) , where f is a mapping from R into a normed vector space. We show stability results of this equation in quasi- β -Banach spaces and (β , p) -Banach spaces. We also prove the nonstability of the previous functional equation in a relevant case. [ABSTRACT FROM AUTHOR]